In seismic surveys, a seismic source is actuated to induce seismic waves at or near the surface of the earth. Explosive sources, vibrating devices and airguns are examples of seismic sources. The seismic waves propagate into and through the earth and are reflected, refracted, and diffracted by geological formations within the earth. Some seismic waves are directed back to the earth's surface, and can be detected by a plurality of seismic receivers (or seismic sensors), such as geophones or hydrophones, deployed at the earth's surface. Each such receiver monitors and records the seismic wavefield at the receiver's location. Typically a receiver monitors the seismic wavefield for a given period after actuation of a seismic source. The data received and recorded by a receiver are in the form of a record of the variation over time of one or more components of the seismic wavefield (such as, for example, the pressure or a component of the particle velocity), and are collectively called a trace. The collection of traces is stored for further processing in known ways to obtain information about the earth's subsurface. Such information is commonly interpreted by geophysicists to detect the possible presence of hydrocarbons, or to monitor changes in hydrocarbon bearing rocks in the subsurface.
FIG. 1 is a schematic illustration of a seismic surveying arrangement that includes a seismic source 1 and five seismic receivers 2-6 spaced from the source 1. FIG. 1 shows a land-based seismic survey in which the seismic source 1 and the seismic receivers 2-6 are provided at the earth's surface. When the seismic source 1 is actuated to emit seismic energy, some of the emitted seismic energy is detected by the seismic receivers 2-6. The receivers measure a component of the seismic wavefield, and provide a data trace showing how that component varies with time.
FIG. 2 is a schematic illustration of traces acquired by the receivers 2-6 of FIG. 1 when the seismic source 1 is actuated to emit seismic energy. Trace X2 is the trace acquired by receiver 2 and so on. (Most seismic receivers in use today are digital receivers that repeatedly sample the seismic wavefield and so output a series of discrete values rather than a continuous trace, but the traces are represented as continuous traces in FIG. 2 for simplicity.) The horizontal axis in FIG. 2 represents the time after actuation of the seismic source 1, and the vertical axis of FIG. 2 represents the offset of the trace (the “offset of a trace is the horizontal distance between the source and the receiver used to acquire the trace). The traces X2 to X6 are arranged in order of increasing offset. Within a trace, the horizontal axis represents the amplitude of the component of the seismic wavefield measured by the receiver, as a function of time.
The traces X2 to X6 represent a “common source gather” of traces. Each trace was acquired following actuation of the source 1.
Each trace X2-X6 contains a number of seismic “events”. Event 7 is the “direct event” and represents the arrival at the receiver of seismic energy that has travelled direct from the source 1 to the receiver 2-6 along the path 8 shown in FIG. 1. Event 9 is a “reflection event”, and represents the arrival at the receiver of seismic energy that was transmitted into the earth's interior and has travelled to the receiver 2-6 along a path such as the path 11 shown in FIG. 1, which involves a reflection at a geological structure 10 within the earth that acts as a partial reflector of seismic energy. The time at which an event occurs in a trace is known as the “arrival time” or the “travel time” of the event, and is equal to the time taken for seismic energy to travel from the source to the receiver via the respective path.
Each of the traces X2 to X6 in FIG. 2 contains a direct event 7 and the reflection event 9. However, the events do not occur at the same times in each trace, because the length of the path of seismic energy from the source to the receiver varies from one trace to another. In the case of the direct event 7, the length of the path of seismic energy from the source to the receiver is equal to the distance from the source to the receiver (i.e. is equal to the offset). The travel time of the direct event therefore varies linearly with offset. In the case of the reflection event 9, however, the relationship between offset and the travel time is not linear—if the velocity of propagation of seismic energy is assumed to be constant and isotropic within the earth then the travel time of the reflection event will, as is well known, show a hyperbolic dependence on offset.
Seismic data in general contains noise signals, which may be coherent or incoherent, as well as the desired seismic reflection signals. These noise signals, hereafter referred as just “noise”, interfere with the interpretation of the seismic signals, and degrade the quality of the subsurface images that can be obtained by processing the recorded seismic data. Travel time readings taken from seismic data traces can also be degraded by travel time fluctuations between traces (known as “time-jitter”). If the traces X2 to X6 of FIG. 2 contain significant random noise and/or time-jitter it would be difficult to make an accurate determination of the travel time of the reflection event 9 occurs. It is therefore very desirable to suppress or attenuate noise and time-jitter that is present in recorded seismic data traces before processing the data to obtain an image of the earth's interior.
One method of attenuating incoherent noise (noise that varies randomly from one trace to another) or time-jitter is to make use of traces in a gather that are adjacent to the trace being processed. For example, if seismic receivers in a seismic survey are deployed close to one another it is likely that the seismic wavefield sampled by a receiver will not be significantly different from the seismic wavefield sampled by an adjacent receiver. However, the incoherent noise or time-jitter will vary randomly from one trace to another. Thus, if adjacent traces are combined the noise and time-jitter in one trace should cancel the noise and time-jitter in another trace (if the noise and time-jitter are random).
In the example of FIG. 2, one method to improve the accuracy of the determination of the travel time of the reflection event 9 in trace X4 would be to make use of the adjacent traces on either side or even of the adjacent two traces on either side. By determining a composite travel time t′ according to:t′=t3+t4+t5   (1)(where tk denotes the travel time of the reflection event 9 in the kth trace) or according to:t′=t2+t3+t4+t5+t6   (2)and subsequently dividing the composite time t′ by the number of traces used in its determination, the effect of random noise on the measured travel time of the reflection event in the trace X4 should be reduced.
As explained above, the travel time of a seismic event varies from one trace to another, and in the case of a reflection event varies non-linearly with offset. It is therefore not possible simply to sum traces acquired at different offsets together. The conventional procedure is therefore to pick the travel time of the event in each data trace, correct the picked travel times for changes in offset, and add the corrected travel times together. This process can be time-consuming. Furthermore, inaccuracy in picking the travel times in the data traces can lead to inaccuracy in the final result.
There are other occasions where it is desired to sum travel times of events in more than one seismic trace. For example, a linear trend removal filter generates a composite travel time according to:t′=−½+tk−1tk−½tk+1 
Again, a linear trend filter is conventionally implemented by picking the individual travel times in individual traces, and summing the picked travel times.